Exponential Combinatorial Extrema

Abstract

We study the following type of problem. For each K we have a family { XiK: i ∈ IK} of random variables which are dependent but identically distributed; and |IK| → ∞ exponentially fast as K → ∞. We are interested in the behavior of \(
{M_K} = {\kern 1pt} {\max _{i \in {I_K}}}{\kern 1pt} X_i^K
\). Suppose that there exists c* ∈ (0,∞) such that (after normalizing the X’s, if necessary)